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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 19
Chapter 3, Problem 19

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-1,3), and (3,4)

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1
Identify the two points given: (-1, 3) and (3, 4).
Calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substitute the points: \( m = \frac{4 - 3}{3 - (-1)} \).
Simplify the slope calculation to find the value of \( m \).
Use the point-slope form of a line equation: \( y - y_1 = m(x - x_1) \). Substitute one of the points (for example, (-1, 3)) and the slope \( m \) into this formula.
Rewrite the equation from point-slope form into slope-intercept form \( y = mx + b \) by solving for \( y \), and then convert it into standard form \( Ax + By = C \) by rearranging terms and clearing fractions if necessary.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope of a Line

The slope measures the steepness of a line and is calculated as the change in y-values divided by the change in x-values between two points. For points (x₁, y₁) and (x₂, y₂), slope m = (y₂ - y₁) / (x₂ - x₁). This value is essential for writing the equation of a line.
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The Slope of a Line

Point-Slope Form of a Line

Point-slope form expresses a line's equation using a known point and the slope: y - y₁ = m(x - x₁). This form is useful for quickly writing an equation when you know a point on the line and its slope, serving as a step toward other forms like slope-intercept or standard form.
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Point-Slope Form

Standard and Slope-Intercept Forms of a Line

Standard form is Ax + By = C, where A, B, and C are integers, and slope-intercept form is y = mx + b, showing slope and y-intercept explicitly. Converting between these forms helps in graphing and analyzing lines, and the problem requires answers in these specific forms.
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